Digital Color Model
Puts Color in a New Light by Ken Davies

The COLORCUBE is a three-dimensional model by which
one can understand and teach digital color theory. This elegant representation of color
bridges the gap between additive and subtractive systems of color, and defines the method
by which colors are stored, manipulated, and reproduced using computer technology.

The COLORCUBE is patented in the United States and
patent-pending internationally.

Introduction

More consumers than ever are buying their way into the digital imaging
market. Digital cameras, color printers and color scanners have become less expensive and
therefore, more accessible to new users. Accompanying this revolution in color usage is
the need to understand digital color and its inherent complexity.

Research indicates that typical end-users are baffled by the intricate
behavior of color and often complain that "the colors that print do not match what is
on the monitor".

In spite of astounding technological advances in color, it is readily
apparent that few people understand the theory of how digital color works. This inability
to fully comprehend new color technologies can lead to customer dissatisfaction and
products that fall short of user expectations.

Spittin' Image Software introduces a new "low-tech" invention
designed to explain the principles of digital color. This recently U.S.-patented device,
aptly named the COLORCUBE, serves as a physical model of how color is stored,
manipulated, and reproduced using digital processes.

Included with the COLORCUBE is a manual describing the 10 steps
to understanding digital color. The following description is provided as an overview:

1) How the Human Eye sees Color

The eye contains two kinds of receptors: rods and cones. While the rods
convey shades of gray, the cones allow the brain to perceive color hues. Of the three
types of cones, the first is sensitive to red-orange light, the second to green light and
the third to blue-violet light. When a single cone is stimulated, the brain perceives the
corresponding color. That is, if our green cones are stimulated, we see "green".
Or if our red-orange cones are stimulated, we see "red". If both our green and
red-orange cones are simultaneously stimulated, our perception is yellow.

The eye cannot differentiate between spectral yellow, and some
combination of red and green. The same effect accounts for our perception of cyan,
magenta, and the other in-between spectral colors.

Because of this physiological response, the eye can be
"fooled" into seeing the full range of visible colors through the proportionate
adjustment of just three colors: red, green and blue.

Spectral Sensitivity Curve for each of the cones in
the human eye.

2) Identifying Primary Colors

Any color can be spectrally analyzed using a prism to determine its red,
green and blue primary values (additive color space), or its cyan, magenta and yellow
primary values (subtractive color space). This simple yet powerfultechnique can be used to
identify true primary colors. Choosing the correct three primaries maximizes the number of
colors reproducible within a color space.

Viewing these circles through a prism reveals the
primary colors. The circle on a white background breaks into Cyan/Magenta/Yellow
primaries. The same circle on a black background breaks into Red/Green/Blue primaries.

3) Additive and Subtractive Color

Televisions, cameras, scanners and computer monitors are based on the
additive system of color (RGB), where red, green and blue light projected together yield
white. Offset printing, digital printing, paints, plastics, fabric and photographic prints
are based on the subtractive system of color (CMY/CMYK) in which cyan, magenta and yellow
mix to form black (K).

The unique feature of the COLORCUBE is that both systems are
integrated within one model. Switching between RGB and CMY color systems is as simple as
turning the model over.

RGB and CMY vertices, when placed in the same referential color
space, form the outer dimensions of a cube.

4) Color Models

With each color theory advancement comes a new model by which to
understand it. Unfortunately, users of older color technologies rarely, if ever, adopt
these new models. For example, the color wheel is virtually identical in appearance and
operation to how it was first conceived by Sir Isaac Newton. Painters continue to
incorrectly define primary colors as red, yellow and blue according to the color wheel
despite the fact that such technologies as offset printing and photography, each almost a
century old, are based on a three-dimensional system of color using the true primaries
cyan, magenta and yellow.

Computers and other digital devices define color based on a new model of
color known as a COLORCUBE, which defines the digital representation of color.

5) Storing Images in Computers

All digital color devices that handle the storage, manipulation, and
reproduction of color images do so by storing RGB values. Digitally storing an image
requires that it first be broken down into a grid of tiny pixels (dots). Each pixel is
sampled for the amount of red, green, and blue light present. The entire image is then
stored one pixel at a time. To store a 3-inch square image at 150 dots per inch requires
storing 202,500 pixels or 607,500 bytes.

The theoretical model describing how colors are stored in a computer is
often displayed as a cube. This method of storing color has proven to be remarkably
adaptive, allowing conversions to a wide variety of color models; including the color
wheel, CIE color space, HSV color, Munsell Sphere, Pantone system, DIN chips, and spectral
definitions of color.

The fundamental difference between the COLORCUBE and all other
models of color is that it describes colors within a color space based on measured input
quantities (what quantities of primary pigments are used to make the color). Other models
of color are based on measured output values (what the color looks like). Basing a color
system on input values considerably simplifies issues related to color naming, color
reproduction, color visualization, color calibration, color manipulation, and color
mapping between color spaces.

6) Visualizing a Color Space

The ability to visualize all the available colors within a
three-dimensional color space and to see the inter-relationships between those colors is a
huge advantage when working with color. Although there are a number of computer diagrams
simulating a theoretical color space, the COLORCUBE model is the first of its kind
to define a physical model with the interior colors visible.

As the eye can see over 16 million colors, the key to the COLORCUBE concept
is that the external edge points of the cube are defined, and interior colors then
approximate the range of colors between end-points. This then defines the outer dimensions
of the visible color space, while allowing the viewer to see the internal elements. Color
cubes of increasing density can then be generated based on a required "total"
number of colors desired. A COLORCUBE that defines all colors reproducible within a
color space would be 256 cubes on each side, for a total of 16,777,216 elements.

Planes of color in 3D color space.

7) Color Mixing

Each color element within a COLORCUBE has a unique numeric
identifier indicating what proportionate input values were used to reproduce the color.
Each element also has a unique position within the cube, thereby ensuring that one can
easily map between positional information and mixing information. If the mixing
information is given, then the positional information can be deduced. If the positional
information is given, then the mixing information can be deduced. This feature of the COLORCUBE
eliminates much of the guess work associated with naming, mixing, and describing a
color, and ensures that within a defined color space, digital colors remain consistently
reproducible.

8) Color Selection

The unique three-dimensional placement of colors within the COLORCUBE
model works well as a color selection tool. Using the cube, it is easy to choose
complementary colors, harmonious color runs, warm colors, cool colors, tints, shades, and
colors of equal value. All color relationships can be shown to be mathematical in nature,
and can be modeled using simple XYZ axis Cartesian math.

9) Color Manipulation

To manipulate colors within a color space one must first define a set of
mathematical rules by which colors can be modified. Color Math, as it is referred
to, relies upon first breaking colors into their constituent primary values, then doing
the mathematical operation. The end result is mixing instructions for a new color that can
be found in the COLORCUBE.

For example, to predict the result of adding two colors together, break
down each color into its primary proportionate values. Then, add together the like primary
values from both colors. The combined total for each primary yields the positional
coordinates for the resulting color within the COLORCUBE. Similar logic can be
applied to color subtraction (subtracting one color from the other), and to higher level
operations such as adjusting contrast, brightness, and saturation.

Color math in subtractive color space:

Equal amounts cyan, magenta and yellow (ABC) yield black (K)

Because of the following:

Equal amounts magenta and yellow yield red

Equal amounts cyan and yellow yield green

Equal amounts cyan and magenta yield blue

Color math can be used to determine that equal amounts
red, green and blue also yield black.

10) Color Mapping and Calibration

The root of all color calibration and color mapping problems is that
color spaces used by different color reproduction processes do not define the same visible
area. Each color space is a subset of the true range of visible colors. To effectively map
colors between different color spaces, a calculation must first be made to determine the
color relationships between each of the color spaces. The objective when mapping colors is
to find the best approximation so that the final image does not appear blatantly altered.

The current solution to correctly mapping colors between two color
spaces requires spectrally analyzing the output characteristics of each device under
controlled lighting conditions, and mapping the colors back to a CIE definition.

Color mapping models in such popular software programs as Corel Photo
Paint, and Hewlett Packard Scanning software, provide two-dimensional color calibration
interfaces which are difficult to use, are incomplete, and require sophisticated knowledge
about color.

Software user interfaces that support color mapping could be vastly
improved by recognizing the three-dimensional nature of color. Color space mappings could
be visually represented in three-dimensional space relative to each other, and relative to
the theoretical set of visible colors.

Conclusion

If a $50,000 digital color system does not perform to expectations, the
end user is likely to conclude they need more training. However, if a $5,000 digital color
system does not perform to expectations, the end user is likely to conclude the product is
broken.

As digital color products become less expensive and sales volumes
increase, the availability of economical product training will become an important issue.
For users to understand how best to recognize and deal with complex color problems, they
must become familiar with the fundamentals of digital color.

The COLORCUBE is an elegant model of digital color which can be
used to teach simple color concepts. Users can learn and properly understand the basic
physiology of color perception, the intricate relationship between additive and
subtractive color systems, and the mathematics of color image manipulation.

At a time when art, science and other color-intensive industries are
converging in the digital realm, a unified vision of color must emerge. The definitive
model for that vision is the COLORCUBE.